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Block #1,901,870

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/19/2016, 2:29:23 PM Β· Difficulty 10.7826 Β· 4,931,667 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
af0e4a2d054bed5375523a755b03ce5f075ef03a45bd4b13e9c93b1d43f39229
View on Chainz β†—

Height

#1,901,870

Difficulty

10.782559

Transactions

2

Size

1.14 KB

Version

2

Bits

0ac855c8

Nonce

1,313,244,141

Timestamp

12/19/2016, 2:29:23 PM

Confirmations

4,931,667

Mined by

⛏️ P2SHAJEPCPfbzJ99EU1JHuTU2zczX5f1QoHhEu

Merkle Root

601ade06f740d89ce111e036df475dfe0158a5eaa2c1deac3df6b4f2eba29257
Transactions (2)
Coinbase1576a1d139a501…a910a5032ac30a
1 in β†’ 1 out8.6000 XPM110 B
AJEPCPfb…f1QoHhEu
cd934e276d7961…4c2a7c35a753a7
6 in β†’ 2 out529.3019 XPM965 B
ATB74oXY…stL4TZyfAWCtK46M…d4PSVabo
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

8.643 Γ— 10⁹³(94-digit number)
86430874333785076237…30573115853066584341
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
8.643 Γ— 10⁹³(94-digit number)
86430874333785076237…30573115853066584341
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.728 Γ— 10⁹⁴(95-digit number)
17286174866757015247…61146231706133168681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.457 Γ— 10⁹⁴(95-digit number)
34572349733514030495…22292463412266337361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.914 Γ— 10⁹⁴(95-digit number)
69144699467028060990…44584926824532674721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.382 Γ— 10⁹⁡(96-digit number)
13828939893405612198…89169853649065349441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.765 Γ— 10⁹⁡(96-digit number)
27657879786811224396…78339707298130698881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.531 Γ— 10⁹⁡(96-digit number)
55315759573622448792…56679414596261397761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.106 Γ— 10⁹⁢(97-digit number)
11063151914724489758…13358829192522795521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.212 Γ— 10⁹⁢(97-digit number)
22126303829448979516…26717658385045591041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.425 Γ— 10⁹⁢(97-digit number)
44252607658897959033…53435316770091182081
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,912,495 XPMΒ·at block #6,833,536 Β· updates every 60s
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